Problem: The light from the moon, in lux, on the night of the $t^{\text{th}}$ day of $2016$, is $ L(t) = 0.25 - \sin\left(\dfrac{2\pi (t-2)}{28.5}\right)$. What is the period of the light from the moon? Give an exact answer.
The period of a function is the amount of time it takes to complete its entire cycle. Since $\sin t$ completes its cycle every time $t$ goes around a whole circle, the period of $\sin t$ is $2\pi$. Every time $t$ increases by $28.5$ days, $\dfrac{2\pi (t-2)}{28.5}$ increases by $2\pi$, so this function repeats every $28.5$ days. The period of the light from the moon is $28.5$ days.